In the given figure, D is mid-point of side BC, the area of triangle BEA is equal to area of triangle :

1. BED

2. CED

3. CEA

4. ACD

In △ ABC,

Since, D is the mid-point of side BC.

∴ AD is the median of BC.

∴ Area of △ ABD = Area of △ ACD (As, median of a triangle divides it into two triangles of equal areas.) ………..(1)

In △ EBC,

Since, D is the mid-point of side BC.

∴ ED is the median of BC.

∴ Area of △ EBD = Area of △ ECD (As, median of a triangle divides it into two triangles of equal areas.) ………(2)

Subtracting equation (2) from (1), we get :

⇒ Area of △ ABD - Area of △ EBD = Area of △ ACD - Area of △ ECD

⇒ Area of △ BEA = Area of △ CEA.

Hence, Option 3 is the correct option.